A particle of mass m is attracted to the origin by a force proportional to the distance from the origin F = -kr. Assume that it moves in circular orbit of radius r.
a) Use Newton's law to show that its kinetic energy 1/2mv^2 equals its potential energy 1/2kr^2.
b) Use Bohr quantum condition on the angular momentum (L = nh) to show that the allowed orbitals are given by r^2 - nh*sqrt(km)
c) Find the allowed energies and show that they can be written E_n = nhf where f is the frequency of revolution.© BrainMass Inc. brainmass.com March 4, 2021, 5:55 pm ad1c9bdddf
F = -k*r = - m*v^2/r = -m*r*w^2 (centripetal force) ......(1)
where, w is angular velocity (rad/s)
=> m*v^2 = k*r^2
=> K.E. = (1/2)*m*v^2 = (1/2)*k*r^2 --Proved
The solution provides step-by-step workings, interspersed with explanatory notes, to showing that the various energies and angular momentums of the described particle can be written a certain way.